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A389782

Expansion of e.g.f. exp( -LambertW(-x*(1+x)) ) / (1+x).

1, 0, 5, 19, 277, 3371, 59881, 1198191, 28559945, 772706071, 23599797901, 801118631963, 29957934034909, 1223466731060211, 54192986947009457, 2587895965559457031, 132543870509509314577, 7247993818694882664623, 421497567638021634991381, 25975285400601822746473011

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OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..350

FORMULA

E.g.f. A(x) satisfies A(x) = exp( x * (1+x)^2 * A(x) ) / (1+x).

a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(k-1,n-k)/k!.

a(n) ~ (4 + exp(1))^(1/4) * 2^(n - 3/2) * n^(n-1) / (exp(n - 9/4) * (sqrt(1 + 4*exp(-1)) - 1)^(n - 3/2)). - Vaclav Kotesovec, Oct 15 2025

MATHEMATICA

Table[n!*Sum[(k+1)^(k-1)*Binomial[k-1, n-k]/k!, {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 01 2025 *)

PROG